Physical forcing of the shelf seas: what drives the motion of ocean? - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 45

Table 2.1. Some of the more important tidal constituents.

Symbol Name Period (hours)

M 2 Principal lunar 12.42

S 2 Principal solar 12.00

N 2 Larger lunar elliptic 12.66

K 2 Luni-solar declinational 11.97

K 1 Luni-solar declinational 23.93

O 1 Larger lunar declinational 25.82

M f Lunar fortnightly 13.7 days

This idea, developed by Lord Kelvin, G. H. Darwin and A. T. Doodson amongst
others, gave rise to the harmonic method of tidal analysis in which the tide is treated
as a sum of independent, sinusoidal tidal constituents. The amplitudes H n and
phase adjustments g n of the constituents are determined by analysis of the observed
tidal elevation using least squares methods (see, for instance, Emery and Thomson,
2001 and book website). Although the number of terms N in the theoretical expan-
sion of the TGF is large (

400), in practice the amplitudes of many of the constitu-
ents are small and the tide can be well represented by a limited number of
constituents (typically

∼

20). A list of a few of the more important tidal constituents
and their frequencies is given in Table 2.1 . Constituents are identified by a symbol
with a letter indicating something about the origin of the constituent and a subscript
denoting the species (1

∼

semi-diurnal). For example, the main semi-
diurnal constituent driven by the Moon (frequently the largest of all constituents) has
the symbol M 2 . Next to this comes the main solar tide S 2 which, because its frequency
is determined by the apparent movement of the Sun, has a period of exactly 12 hours.
In most parts of the ocean the semi-diurnal tides tend to predominate and the
diurnal constituents are relatively small. There is, however, often a tendency for
the two tides in the day to be unequal, an effect which arises from the fact that the
Moon moves above and below the equator over the monthly cycle reaching a
declination (angular height above the equator) which can be as large as 28.5 . When
the Moon is above or below the equator, the axis of the ellipsoid moves with it and
this gives rise to inequality between the two tides during a day which is represented,
for example, in the diurnal constituent O 1 . The Sun also moves above and below the
equator (

¼ diurnal, 2 ¼

23.5 ) so there are similar solar declinational constituents. In a few
areas, the diurnal tendency takes an extreme form with large diurnal constituents
resulting in only one tidal oscillation per day. There are also variations in the tide
associated with the fact that the orbit of the Moon is an ellipse rather than a circle,
which gives rise to 'elliptic' tidal constituents like N 2 which has a longer period than
M 2 and beats with it to produce a monthly variation in tidal range.
As we have just noted, in many areas of the shelf seas, the main lunar and solar
semi-diurnal tidal constituents M 2 and S 2 are the largest. These constituents have
periods of 12.42 and 12 hours and their interaction produces a regular range

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